# Full text of "Analytical Mechanics"

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```IMPULSE AND MOMENTUM                     241
spending component of the resultant momentum of the system changes, that is,
X = ~ (Smz), etc. at
194.  The Principle of the Conservation of Momentum. — When the resultant external force is zero equation (V) gives
or                               2 (rav) = const.                            (VI)
Therefore when the sum of the external forces acting upon a system vanishes the resultant momentum of the system remains constant, both in direction and magnitude. This is the principle of the conservation of momentum. The momenta of the various parts of an isolated system may and, in general, do change, but the vector sum of the momenta of all the particles of the system cannot change either in direction or in magnitude.
PROBLEM.
Show that if the component, along any direction, of the resultant external force vanishes, the corresponding component of the resultant momentum of the system remains constant, that is,
x = const., when X = 0.
195. Momentum of a System. — The magnitude of the re-component of the resultant momentum of a system may be put in the following forms:
2 mi = -r (Sraz) at
= ~~ (Mx) [by equation (I7), p. 141]    £ at
Similarly```